Simplify the following expression: $\dfrac{3z}{4z^4}$ You can assume $z \neq 0$.
$ \dfrac{3z}{4z^4} = \dfrac{3}{4} \cdot \dfrac{z}{z^4} $ To simplify $\frac{3}{4}$ , find the greatest common factor (GCD) of $3$ and $4$ $3 = 3$ $4 = 2 \cdot 2$ $ \mbox{GCD}(3, 4) = = 1 $ $ \dfrac{3}{4} \cdot \dfrac{z}{z^4} = \dfrac{1 \cdot 3}{1 \cdot 4} \cdot \dfrac{z}{z^4} $ $\phantom{ \dfrac{3}{4} \cdot \dfrac{1}{4}} = \dfrac{3}{4} \cdot \dfrac{z}{z^4} $ $ \dfrac{z}{z^4} = \dfrac{z}{z \cdot z \cdot z \cdot z} = \dfrac{1}{z^3} $ $ \dfrac{3}{4} \cdot \dfrac{1}{z^3} = \dfrac{3}{4z^3} $